Singular symplectic surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914410408181760 |
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| author | Garbagnati, Alice Penegini, Matteo Perego, Arvid |
| author_facet | Garbagnati, Alice Penegini, Matteo Perego, Arvid |
| contents | In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $σ$ on the smooth locus, and for which every finite quasi-étale covering has the algebra of reflexive forms spanned by the reflexive pull-back of $σ$. We moreover prove that the Hilbert scheme of two points on such a surface $X$ is an irreducible symplectic variety, at least in the case where the smooth locus of $X$ is simply connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular symplectic surfaces Garbagnati, Alice Penegini, Matteo Perego, Arvid Algebraic Geometry 14B05, 14J28, 14J42, (14E20, 14N20) In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $σ$ on the smooth locus, and for which every finite quasi-étale covering has the algebra of reflexive forms spanned by the reflexive pull-back of $σ$. We moreover prove that the Hilbert scheme of two points on such a surface $X$ is an irreducible symplectic variety, at least in the case where the smooth locus of $X$ is simply connected. |
| title | Singular symplectic surfaces |
| topic | Algebraic Geometry 14B05, 14J28, 14J42, (14E20, 14N20) |
| url | https://arxiv.org/abs/2407.21173 |